The applicant's previous applications and provisional applications, including, but not limited to, U.S. patent application Ser. No. 12/018,069, filed. Jan. 22, 2008, entitled “Wireless Apparatus and Methods”, the disclosure of which is herewith incorporated by reference, describe wireless transfer of power. The transmit and receiving antennas of one exemplary embodiment are resonant antennas, which are substantially resonant; e.g., within 10% of resonance, 15% of resonance, or 20% of resonance. The antenna of an exemplary embodiment is of a small size to allow it to fit into a mobile, handheld device where the available space for the antenna may be limited. An exemplary embodiment describes a high efficiency antenna for the specific characteristics and environment for the power being transmitted and received. Antenna theory suggests that a highly efficient but small antenna will typically have a narrow band of frequencies over which it will be efficient.